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Alpha and Beta Companies can borrow for a five-year term at the following rates: Alpha Beta Moody’s credit rating Aa Baa Fixed-rate borrowing cost 10.5% 12.0% Floating-rate borrowing cost LIBOR LIBOR + 1% a. Calculate the quality spread differential (QSD). b. Develop an interest rate swap in which both Alpha and Beta have an equal cost savings in their borrowing costs. Assume Alpha desires floating-rate debt and Beta desires fixed- rate debt. No swap bank is involved in this transaction. Assume the party, who pays floating- rate to his counterparty, needs to pay LIBOR

Question

Alpha and Beta Companies can borrow for a five-year term at the following rates: Alpha Beta Moody’s credit rating Aa Baa Fixed-rate borrowing cost 10.5% 12.0% Floating-rate borrowing cost LIBOR LIBOR + 1% a. Calculate the quality spread differential (QSD). b. Develop an interest rate swap in which both Alpha and Beta have an equal cost savings in their borrowing costs. Assume Alpha desires floating-rate debt and Beta desires fixed- rate debt. No swap bank is involved in this transaction. Assume the party, who pays floating- rate to his counterparty, needs to pay LIBOR

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Solution

a. The Quality Spread Differential (QSD) is calculated by taking the difference between the borrowing costs of two companies. In this case, we are comparing Alpha and Beta companies.

Alpha's fixed-rate borrowing cost is 10.5% and Beta's is 12.0%. Therefore, the QSD is 12.0% - 10.5% = 1.5%.

b. To develop an interest rate swap where both Alpha and Beta have equal cost savings in their borrowing costs, we need to consider that Alpha wants floating-rate debt and Beta wants fixed-rate debt.

Alpha can borrow at a fixed rate of 10.5% and Beta can borrow at a floating rate of LIBOR + 1%.

In the swap, Alpha would agree to pay Beta a fixed rate (lower than 12.0%) and in return, Beta would pay Alpha the floating rate of LIBOR. The fixed rate that Alpha pays to Beta would be determined such that the cost savings for both parties are equal.

For example, if the fixed rate that Alpha pays to Beta is 11.25%, then both parties would save 0.75% on their borrowing costs. Alpha's cost would be LIBOR (from the swap with Beta) compared to its original cost of 10.5% fixed rate, and Beta's cost would be 11.25% (from the swap with Alpha) compared to its original cost of LIBOR + 1% floating rate.

Please note that the exact fixed rate that Alpha pays to Beta in the swap would depend on the specific terms agreed upon by both parties.

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